Based on the scaling laws, how many times greater is the strength-to-weight ratio of a nanotube (D = 10 nm) than the leg of a flea (D = 100 μm)? Than the leg of an elephant (D = 2m)?

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28-01-2020
Physics

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Based on the scaling laws, how many times greater is the strength-to-weight ratio of a nanotube (D = 10 nm) than the leg of a flea (D = 100 μm)? Than the leg of an elephant (D = 2m)?

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cjmejiab cjmejiab · Answer 1 · 2020-01-29T19:53:38+01:00

To solve this problem we will apply the laws of proportion between the resistance / weight ratio that may occur depending on the cases mentioned. The strength-to-weight ratio for each object is,

For the nano tube,

[tex]\frac{S}{W} = \frac{1}{10*10^{-9}} =1*10^{8}[/tex]

For the leg of a flea,

[tex]\frac{S}{W}= \frac{1}{100*10^{-6}}=10000[/tex]

For the elephant,

[tex]\frac{S}{W} = \frac{1}{2}= 0.5[/tex]

From this we can conclude that the resistance / weight ratio of the nano tube is 10 thousand times better than the flea's leg and [tex]10 ^ 8[/tex] times better than the elephant's leg.